Simple Air Filter questions

I doing first time maintenance on the air filter and, boy the foam cover was caked. Washed it out with soap/degreaser and water till foam is clean. Paper filter looks pretty good. Tapped it and shook it to get out loose dirt and dust. My question is that I need to re-oil the foam cover. Can I use synthetic oil? The manual recommends some specialized filter oil. Is this necessary? Synthetic is all I’ve got and I’m 25 miles for my dealer. Please advise. Also is any after market air filter really any better than stock?